Sure, you can play him however you like. Gunzerking regens your health and your ammo, so you could quite happily play conservative, blasting away and keeping out of trouble. If you get in trouble, either taking too much damage or running low on bullets, you pop gunzerking and the problem solves itself.

Sure, Gunzerking makes you want to charge in like a madman and gun down everything in a cackling hail of death. Doesn't mean you have to, or that it's the only way to play.
Disclaimer; I Have barely played Salvador even as far as Flint.